Colton looks around at an assembly. he notices his younger sister to his right and his older brother 7 feet ahead of him. if colton's brother and sister are 8 feet apart, how far apart are colton and his younger sister? if necessary, round to the nearest tenth.

The solution are-

(a) lim h (x) = -2

   x → -2⁻

(b) lim h (x) = -2

   x → -2⁺

(c) lim h (x) = -2

   x → -2

A limit describes the value which a function approaches as its inputs get increasingly closer to a certain number.

The concept of a limit is at the heart of all calculus.

(a) lim h (x) = -2

   x → -2⁻

Put x = 2 at the place of x in h(x).

This limit is called the left hand limit of the function as there is negative sign over 2.

(b) lim h (x) = -2

   x → -2⁺

Put x = 2 at the place of x in h(x).

This limit is called the right hand limit of the function as there is positive sign over 2.

(c) lim h (x) = -2

  x → -2

Put x = 2 at the place of x in h(x).

This limit exists just at x = 2.

To know more about the limits of the functions, here

https://brainly.com/question/23935467

#SPJ9

For given relations, relation (1) and relation (3) represent y as a function of x.

And relation (2) does not represent y as a function of x.

In this question, we have been given some relations.

We need to determine which relations represent y as a function of x.

We know that a relation is function when there is unique output for each input.

Consider the first relation.

y = -3.4x

For each value of x there's unique and distinct output. Here x can take any real value.

so, the above relation is a function.

Consider the second relation.

We can observe that, for x = 1 there are two outputs i.e., y = 1 and y = -1.

Similarly for x = 4, there are two outputs y = 2 and y = -2.

this means, the second relation is not a function.

Now, consider the last relation.

From this graph we can see that from x = -∞ to x = ∞, there are unique outputs.

So, above graph represents a function.

Also, by vertical line test, the graph represents a function.

Therefore, for given relations, relation (1) and relation (3) represent y as a function of x.

And relation (2) does not represent y as a function of x.

Learn more about the function here:

https://brainly.com/question/28278699

#SPJ1

Answer:

Each pencil costs $2

Step-by-step explanation:

3p + 6 = 12

3p = 6

p = 2

3 pencils for 2 dollars is 6 dollars, plus the 6 dollars he spent on a notebook, equals the 12 dollars he spent total.

Answer:

True.

Step-by-step explanation:

(LHS) cos 6∘ cos 42∘ cos 66∘ cos 78∘

1/4 [cos(66∘+6∘) = cos(66∘-6∘)] • [cos(78∘+42∘)+cos(78∘-42∘)]

= 1/4(sin18∘+12)(-12+cos36∘)

[∵cos72∘ = cos(90∘−18∘) = sin18∘]

1/4[(5-√-1)/4+1/2][−1/2+(5-√+1)/4]

[∵sin(18∘ = (5-√-1)/4, and, cos 36∘ = (5-√+1)/4]

1/4(5-√+1)/4(5-√-1)/4 = (5-1)/64

= 4/64 = 1/16 (RHS)

Therefore, the cosine is equal to 1/16.

Answer: Taxi driver has at most $10 to spend on the cab ride, he can travel at most 12.7 miles.

Step-by-step explanation:

A Taxi driver charges a flat rate = 7.25 dollars

taxi fare for 1 mile = 0.65 dollars

Suppose we consider Total money taxi driver can spend = 10 dollars

Let taxi driver travel x miles

Total charges = flat rate charge + taxi fare for each mile(distance) travelled

Find the value y = [?] + [?]x

suppose these two question marks indicate z1,z2

replace with y=10 and z1=1.75 and z2=0.65 values

Then y = [z1] + [z2]x

10 = 1.75 + 0.65(x)

0.65(x) = 10 - 1.75

0.65(x)= 8.25

x = 8.25/0.65

x = 12.7 miles

If Taxi driver has at most $10 to spend on the cab ride, he can travel at most 12.7 miles.

Learn about more information https://brainly.in/question/33655852

#SPJ9

Answer:

5729627829263#wyyeiwyuwityeioe

Joe is going to [tex]12[/tex] minutes and [tex]18[/tex] seconds to ascend to the Sears tower's roof from street level.

Speed indicates how quickly something or someone is moving. Speed is calculated as follows: speed = distance * time. Following are the relationships between time, distance, and speed: Distance is directly related to speed and time. Time and speed are also negatively related. Speed is what it means. the speed at which an object's location changes in any direction. The distance traveled in relation to the time it took to travel that distance is how speed is defined. Since speed simply has a direction and no magnitude, it is a scalar quantity. Distance is the sum of an object's movements, regardless of direction. The flow of events from the past into the future is known as time. Time only ever moves in one way. Time can go either forward or backward, but not both.

To learn more about speed, time and distance, click here:

https://brainly.com/question/9834403

#SPJ4

The equations ordered from the least to greatest is

y = (-3/4)x + 2

y - 3 = 1/2(x - 4)

3x - 4y = 7

y = 12(x - 19) + 5

From the question, we are to order the equations from least to greatest by the value of the slope

The given equations are

y = (-3/4)x + 2

3x - 4y = 7

y = 12(x - 19) + 5

y - 3 = 1/2(x - 4)

To determine the slopes of the line, we will compare the equations to the general form of the equation of a line

The general form of the equation of a line is

y = mx + b

Where m is the slope

and b is the y-intercept

By comparison,

m = -3/4

∴ Slope = -3/4

First, rearrange

3x - 7 = 4y

4y = 3x - 7

y = (3/4)x - 7/4

By comparison,

m = 3/4

∴ Slope = 3/4

First, simplify

y = 12x - 228 + 5

y = 12x - 223

By comparison,

m = 12

∴ Slope = 12

y - 3 = 1/2(x - 4)

First, simplify

y - 3= (1/2)x - 2

y = (1/2)x -2 + 3

y = (1/2)x + 1

By comparison,

m = 1/2

∴ Slope = 1/2

Now,

The slopes ordered from the least to greatest is

-3/4 < 1/2 < 3/4 < 12

Thus,

The equations ordered from the least to greatest is

y = (-3/4)x + 2

y - 3 = 1/2(x - 4)

3x - 4y = 7

y = 12(x - 19) + 5

Learn more on Order of equations here: https://brainly.com/question/9353038

#SPJ1

The equation can be summarized as; p = $50 + 3($100 ). Hence William was paid $350.

A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0.

Let p represents the paycheck.

William  paid her parents $50 for rent. After paying the rent he evenly divided the rest of the amount into three parts.

He puts $ 100 into her savings account. It means that he also puts $100 into checking account and $ 100 into retirement fund

If we put the parts together, the equation we get is;

p = $50 +$100 +$100 +$100

The equation can be summarized as;

p = $50 + 3($100 )

Now we can easily find how much was William  paid;

p = $50 + 3($100)

p = $50 +$300

p = $350

Hence William was paid $350.

Learn more about linear equations;

https://brainly.com/question/10413253

#SPJ4

Answer:

1. right

2. obtuse

Step-by-step explanation:

Answer:

Acute and obtuse

Step-by-step explanation:

The first picture is acute as the angle is less than 90 and the second picture is obtuse as the angle is greater than 90 but less than 180.

Answer: 6

Step-by-step explanation:

got it right

Answer: -118

Step-by-step explanation:

49^((1)/(2))- 25^((3)/(2))=

49^(1/2) -25^(3/2)=

7-25^((2+1)/2)=

7-25^((2/2)+(1/2))=

7-25^(1+1/2)=

7-25^(1) *25^(1/2)=

7-(25*5)=

7-125=-118

Answer: car a must be meet to cannot be so your aner is a

Step-by-step explanation:

Answer:

The absolute value of a number is the distance between the number and zero on a number line. Every number and it opposite are the same distance from zero on the number line.

There are 5354 people were in the arena.

Percentage:

The term percentage is referred as a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100.

The formula for calculating the percentage is,

Percentage = (Actual value/Total value) x 100

Given,

Here we have that, 4550 men in the arena comprised 85% of the people in the arena.

Now we need to find how many people were in the arena.

Let p be the number of people in Arena.

So, based on the percentage formula,

It can be written as,

=> 85% = (4550 / p) x 100

=> 85/100 = 4550 /p

=> 0.85 = 4550/p

=> 4550/0.85 = p

=> p = 5354

Therefore, there are 5354 people were in the arena.

To know more about Percentage here.

https://brainly.com/question/28269290

#SPJ4

Answer:

A. No solution

Step-by-step explanation:

Please see attachment for the graph.

Hope this helps!

Please mark as brainliest if correct!

The equation has No Solution.

The points at which the lines representing the intersection of two linear equations are defined as the solution to a linear equation. In other words, the set of all possible values for the variables that satisfy the given linear equation is the solution set for the system of linear equations.

The set of linear equations can be solved in one of three ways

Unique Solution, No Solution and Infinitely Many Solutions.

Given equations

2x + 6y = 12

x   0    6  

y   2    0

6x + 18y = 18

x   0    3  

y   1    0

The graph of equations is attached,

for solution of equation,

we can find it by graph, the graph shows the parallel line for both equation since equations have No Solution.

The system of linear equations does not have a solution if the graphs of the linear equations are parallel. In this instance, there is no point at which lines do not cross.

Hence there is no solution for equations.

Learn more about solution of equation;

https://brainly.com/question/545403

#SPJ2

Answer:

the AED450

Step-by-step explanation:

I don't know what to say about my answer but I think it's just the best way to anwers

The mean of a set of final scores from a recent outing is 50.77

Here,

A group of friends enjoys playing miniature golf together.

Here are a set of final scores from a recent outing:

39, 41, 44, 50, 54, 56, 56, 56, 61  

We have to find the mean.

What is Mean?

The mean of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set.

Now,

Set of final scores from a recent outing:

39, 41, 44, 50, 54, 56, 56, 56, 61

Then, Mean =  39 + 41 + 44 + 50 + 54 + 56 + 56 + 56 + 61 / 9

                   = 457/9

                   = 50.77

Hence,

The mean of a set of final scores from a recent outing is 50.77

Learn more about the mean visit:

https://brainly.com/question/1136789

#SPJ4

=50

Step-by-step explanation:

=1/2×100

=1×50

=50

Answer:

A

Step-by-step explanation:

The two sentences relate like They establish a contrast. As  American Sleep Disorders Association is considering the teenager sleep and adult sleep.

What is sleeping disorder?

Sleep Disorders are mostly common nowadays as people are more busy in their scheduling, they don't get proper and sufficient time to sleep. This creates many problems in the human body.

The common type of sleeping disorder are  insomnia, restless toughnesses' syndrome, narcolepsy and sleep apnea.

Thus, option A is correct.

For more details about sleeping disorder, click here:

      Of all of the common assumptions that we discussed in class, I think one of the most common is the idea that a children’s text should in some way teach the reader something.  We of course talked about the term didactic, and how a didactic book strongly pushes a lesson onto the reader, telling them that they should believe this or that.  Many times a reason for that lesson isn’t even given, as though the young person reading the book should just accept that lesson because they are told to, because the other knows better.  As I was reading Cat in the Hat by Dr. Seuss, the book I selected for the assignment, I was hoping that it wouldn’t be as didactic as most other children’s books, and that it would be as playful and exciting as I remember as a child.  On the last two pages of the book, however, the absent mother returns home, the cat has disappeared, the children are behaving nicely, sitting in chairs, and it is pretty obvious that even though they got into mischief they are still good children after all.  Nothing really has changed at the end of the book.  Although all sorts of things got played with, and the children broke the rules I am sure they know about (like, “Don’t fly kites in the house”), major boundaries were never crossed.

           We talked about how the opposite of a didactic book might be an ambiguous book, or a book that encourages the reader to think about issues, to make decisions for themselves.  In that kind of book, the author usually wants to the reader to think for her or himself, to understand that some things are difficult, even for adults.  The author may present a problem and ask you what you think, or might just never come around to saying exactly what you are supposed to believe.  The last page of Cat in the Hat ends with the narrator saying, referring to the mother, “Should we tell her about it? / Now what SHOULD we do? / Well . . . / What would YOU do / If your mother asked you?” (61).  In some ways, this is probably a pretty ambiguous ending.  The author asks the reader that if your mother left, if someone wanted you to do what you weren’t supposed to, if you did it anyway, and if you didn’t get caught, then would you tell your mother or father what happened?  Most adults wouldn’t tell what happened themselves, but the question is there anyway, and it seems to be really asking children what they believe.

           But it doesn’t seem really that ambiguous.  If the book were really ambiguous it would be breaking the Typical Case Prototype of children’s books, and in almost every other way the book keeps to those prototypes.  As Nodelman describes it, children’s books are typically bright, colorful, funny, entertaining, and maybe sometimes rhyming.  Children’s books portray children as the way adults typically think of them, as crazy kids who aren’t serious like adults, or innocent angels who would never really do any harm when they play.  Dr. Suess portrays typical kids, bored by the rain, wanting to do something wild.  Although Seuss’s style is strange, the children even look like the sort of standard white children that appear in most books, the girl in a dress and ribbon in her hair.  We saw in class how these children are a lot like the standard one’s in Cassie’s history textbook  And although strange things happen in the book – a talking cat, a couple of strange Things, a lot of things getting thrown around – it is the kind of play we come to expect in children’s lives, especially in the sorts of standard things shown on television and in movies.

           In fact, the children never quite seem to trust the Cat, and they always just sort of watch him play.  The children never really do anything that crazy themselves.  The Fish, who sounds a lot like an adult, is always there to warn them, and in the end everything gets cleaned up.  Of course the book is fun and playful, and is obviously one of the most famous and liked picture books ever made, but it is still pretty straightforward.  Cat in the Hat reinforces and demonstrates almost all of the typical assumptions about childhood, and it fulfills all of the typical case prototypes of children’s books.  Examining it made me think about how the book might have changed in recent years, especially since children are rarely bored when they are at home any more (with all of the stuff they own to play with).  But more than that, it made me think about why we expect all children’s books to be like this, why it is always considered one of the best books for children.  Although I like typical children’s books, it makes me also interested in books that don’t do what we expect.  The book was written 1957, and in so many ways children’s books have become so incredibly different since then.  But in a lot of other ways, some good, some bad, they haven’t changed at all.    

The six trigonometric functions of theta for the point (-4, -4) is

sin Θ = -1/√2

cos Θ = -1/√2

tan Θ = 1

cosec Θ = -√2

sec Θ = -√2

cot Θ = 1

Trigonometric Functions:

Trigonometric functions are defined as the functions of an angle of a triangle. It means that the relationship between the angles and sides of a triangle.

The six trigonometric functions are,

Sin Θ =Opposite/Hypotenuse

Cos Θ = Adjacent/Hypotenuse

Tan Θ = Opposite/Adjacent

Sec Θ =  Hypotenuse/Adjacent

Cosec Θ  = Hypotenuse/Opposite

cot Θ  = Adjacent/Opposite

Given,

Let (-4,-4) be a point on the terminal side of theta in standard position.

Here we need to find the exact values of six trigonometric functions.

Here the give point (-4,-4) represents the values of (opposite, adjacent).

So, the opposite = -4

and adjacent = -4

Now we have to find the hypotenuse of the point,

For that, we have to use the Pythagoras theorem,

hypotenuse = √oppostie² + adjacent²

Therefore,

=> hypotenuse = √(-4)² + (-4)²

=> hypotenuse = √16 + 16

=> hypotenuse = √32

it can be written as,

=> hypotenuse = √2 x 16

=> hypotenuse = 4√2

Now the six trigonometric functions are based on the formula,

sin Θ = -4/4√2 => sin Θ = -1/√2

cos Θ = -4/4√2 => cos Θ = -1/√2

tan Θ = -4/-4 => tan Θ = 1

cosec Θ = 4√2/-4 => cosec Θ  = -√2

sec Θ = 4√2/-4 =>  sec Θ  = -√2

cot Θ = -4/-4 => cot Θ = 1

So, all the six trigonometric values are identified.

To know more about Trigonometric functions here.

https://brainly.com/question/14434745

#SPJ4

Answer:

Step-by-step explanation:

3^2+4^ / 3-4 = -25

The solution set of the inequality is the set of all real numbers larger than 5, written in interval form as (5, ∞)

Here we have a simple inequality:

x - 2 > 3

To solve this we need to isolate x in one side of the inequality.

Now, remember that we can do the same operation in both sides of the inequality. So, if we add in both sides the same number, then the truth value of the inequality does not change.

Then if we add 2 in both sides of the inequality we get:

x - 2 + 2 > 3 + 2

x  > 5

Then the solution set of the inequality is the set of all real numbers larger than 5, written in interval form as (5, ∞).

If you want to learn more about inequalities:

https://brainly.com/question/24372553

#SPJ1

Refer to the image for the graph of the lines.

The common form of the equation of a line is y = mx + c, where m is the slope of the line and c is a constant.

We need to draw any line with a slope m = 2, and

another line with a slope m = -2.

Disclaimer: Let us assume that the constant c = 0.

Then the equation to the line with a slope of "positive" 2 is given by

y = 2x

Then the equation to the line with a slope of "negative" 2 is given by

y = -2x

Refer to the attached image for the graph of the lines with the slope of "positive" 2 and "negative" 2.

f: green line indicates a line with a slope of "positive" 2.

g: blue line indicates a line with a slope of "negative" 2.

Learn more at:

https://brainly.com/question/28360812

#SPJ9